Navigation method

ABSTRACT

Method and apparatus for moving ahead the impact point of a projectile, such as a torpedo, equipped with a passive search head and steered by controlling the rate of change of heading. The projectile, during the autonomous phase, is steered by proportional navigation and, in the vicinity of the target, is switched over to navigation on a deviated pursuit course, the squint, or deviation, angle being such that the first point of intersection of the spiral path with the track being made good by the target is approximately amidship of the target. At the instant of switch-over from proportional navigation to a deviated pursuit course navigation, the amplification factor of the control circuit is switched to ONE, and there is applied to the control circuit a constant d.c. voltage, throughout a predetermined, finite time interval to simulate an additional bearing change.

States Unite atet [191 Ammon NAVIGATION METHOD Werner Ammon, Frankfurt am Main, Germany [75] Inventor:

[73] Assignee: Licentia-Patent-Verwaltungs- G.m.b.H., Frankfurt am Main, Germany [22] Filed: Sept. 20, 1971 [21] Appl. No.: 182,198

52 U.S. Cl. 114/23; 114/25 [51] Int. Cl... F42b 19/06; F42b 19/01; F42b 19/10 [58] Field of Search 114/23, 25

[56] References Cited UNITED STATES PATENTS 2,996,028 8/1961 Montgomery et al. 114/25 2,996,029 8/1961 Jones 114/25 Primary ExaminerBenjamin A. Borchelt Assistant ExaminerThomas H. Webb Attorney, Agent, or Firm-Spencer & Kaye [57] ABSTRACT Method and apparatus for moving ahead the impact point of a projectile, such as a torpedo, equipped with a passive search head and steered by controlling the rate of change of heading. The projectile, during the autonomous phase, is steered by proportional navigation and, in the vicinity of the target, is switched over to navigation on a deviated pursuit course, the squint, or deviation, angle being such that the first point of intersection of the spiral path with the track being made good by the target is approximately amidship of the target. At the instant of switch-over from proportional navigation to a deviated pursuit course navigation, the amplification factor of the control circuit is switched to ONE, and there is applied to the control circuit a constant dc voltage, throughout a predetermined, finite time interval to simulate an additional bearing change.

5 Claims, 6 Drawing Figures (NORTH) TARGET G 3,896,751 7 PATtNTEDJULZSIHYS SHEET 1 (NORTH NORTH) TARGET s 'Hdisf I J 56 57\ SHEET PATENTEB JUL2 9 i975 NAVIGATION METHOD BACKGROUND OF THE INVENTION Practically all modern torpedoes are equipped with an acoustic search head, operating on the sonar principle, which, when the torpedo is sufficiently close to the target, takes over the guidance of the torpedo in the final phases of its travel toward the target. The sensor which picks up the target and from which there is obtained a signal that is utilized to produce the control signals which actually steer'the projectile is normally in the form of a pivotally mounted antenna which is built into the nose of the projectile. Such an antenna is connected to an automatic follow-up system which trains the antenna on the target and keeps it trained on the target regardless of what movements the target and the projectile carry out. Such antennas are said to be locked on the target, i.e., the main axis of the directional lobe of the antenna is directed toward the target. If the main axis is, at any time, not directed toward the target, the return signal will strike the antenna at an angle 111 this being the angle of incidence of the returned signal. This angle is sensed and measured, and an appropriate signal is applied to a follow-up system or servo loop which turns the antenna until the signal representing the angle #1,, is equal to zero, whereupon the follow-up system ceases to move the antenna. In practice, the follow-up system responds so fast that the antenna can easily be kept trained on the target.

The position of the main axis of the antenna can be measured with respect to a spatially fixed reference direction, for example, with the help of a gyro, and the thus determined angle between the orientation of the main axis and the reference direction will be the bearing of the projectile toward the target. If, instead of a directional gyro, a rate-of-turn gyro is used, the change in the bearing can be measured.

In case of torpedoes, until the same are close enough to the target to enable the search head initially to pick up or acquire the target, the torpedo is generally controlled via a cable, one end of which is connected to the torpedo and the other end of which unwinds from a coil aboard the launching vessel, where the cable is connected with a fire control computer that sends command signals to the guidance system carried aboard the torpedo.

The computer aboard the launching vessel will normally operate according to one of the following meth ods:

A. The collision course or intercept method, where the torpedo is fired with a suitable lead so as to intercept the target. This method can be carried out if the course and speed of the torpedo launching vessel as well as the target are known; if the target maintains constant course and speed, the torpedo will follow a straight line.

B. The line-of-sight method, which can be used when the above information is not available, as is the case, for instance, when the launching vessel uses only passive direction finding means, such as passive sonar, and uses only the information derived from this passive sonarwhich is normally limited to the bearing of the targetrelative to the launching vessel and whether or not the target is approaching-to fire the torpedo at the approaching target. According to the line-of-sight method, the torpedo will travel along a trajectory that coincides with a line drawn between the launching vessel and the target at any instant.

After the torpedo has come sufficiently close to the target, the torpedo guidance system is switched over and comes under the control of the search head carried by the torpedo, so that the torpedo is now entirely on its own. During this autonomous phase of the operation, the torpedo is controlled by so-called proportional navigation, the control circuit operating in accordance with the following mathematical formula:

1. 111,,,=K,,1l1,,, differential form 2. rp,,,=K,,|,,,+tl1 integral form where 111, is the nominal heading of the projectile, ill is the angle between true North and the line of sight between the projectile and the target, and K is a navigation constant. All angles d: are taken with respect to true North; 41 is the first derivative of ll! with respect to time, namely. the rate of change of heading.

One conspicuous drawback of torpedoes being steered by a torpedo-borne, passive sonar type guidance system is that the torpedo will always approach the noise source which is to be found in the wake of the enemy ship aft of the screw. Consequently, the torpedo will either miss or will strike the target ineffectively from the aft position.

During the Second World War, therefore, torpedoes were guided along a pure pursuit course, this being a special case of proportional navigation. If the navigation constant K,,=l and 41 0, the torpedo will approach the target from precisely the aft direction. In many cases, the torpedo can be made to strike the target more nearly amidship instead of at the screw by superimposing a sinusoidal serpentine motion.

According to a further modification of the proportional navigation, the navigation constant is again K,,=l but there is provided a constant angle of deviation 111 a 0. When the projectile is guided according to this condition, there is obtained the well-known squint or oblique curve.

The purse pursuit and the oblique paths are no longer used today during the autonomous phase of the operation of a projectile when the same is being guided by the equipment carried aboard the projectile. Instead, the presently preferred proportional navigation uses a navigation constant K,, l, namely, a constant from 5 to 10, as a result of which the projectile is made to travel along a collision course with the target.

The above-mentioned drawback, namely, that the torpedo, if equipped with a passive sonar type search head, will seek out the source of the noise and hence the turbulence left by the wake of the screw, is still present. Since the torpedo, while being guided toward the target on a collision course, will generally approach the target not from directly astern but at a certain angle, little purpose would be served to superimpose the above-mentioned sinusoidal serpentine motion to the torpedo, particularly since there is the danger that the torpedo might happen to be on the wrong side of the serpentine path just as it reaches the target.

One way to overcome the above drawback would be to provide a method for displacing, and, more particularly, for moving ahead, the impact point of an autonomously quided projectile having a passive sonar type search head and being guided under proportional navigation wherein the navigation constant in the guidance system K,, l, by impressing, in the vicinity of the target, an additional dc. voltage to the input of the guidance controller, the amplitude of which dc. voltage is dependent on the basic deflection and, if desired, on the distance of the projectile from the target. The additional dc. voltage causes the projectile to leave the constant bearing course in order to hit the target more nearly amidship. Experience has shown, however, that the system is very sensitive to the parameters.

Another way of accomplishing the desired result would be to switch over from proportional navigation to a deviated pursuit course in the vicinity of the target, in such a way that the first intersection of the spiral path with the track being made good by the target is approximately amidship of the target. This, too, has given rise to problems on how satisfactorily to accomplish this result, and it is the primary object of the present invention to provide an acceptable and practical solution.

SUMMARY OF THE INVENTION With the above object in view, the present invention provides a method and apparatus for moving ahead, i.e., advancing the impact point of a projectile, such as a torpedo, which is equipped with a passive search head and is steered by controlling the rate of change of heading. The projectile, which, during the autonomous phase, is steered by proportional navigation, is switched over, in the vicinity of the target, to a deviated pursuit course navigation, the squint angle being such that the first point of intersection of the spiral path the track being made good by the target is approximately amidship of the target. The point in the vicinity of the target at which the switch-over takes place can be determined by the distance measuring arrangement shown in applicants copending US. patent application Ser, No. 763,4!4 filed Sept. 27, 1968, now abandoned. In accordance with the present invention, at the instant of switch-over from proportional to navigation along a deviated pursuit course, the amplification factor of the control circuit is switched to ON E, and there is applied to the control circuit a dc. voltage through a predetermined, finite time interval.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a typical tactical situation involving a projectile and a target.

FIG. 2 is a block diagram of a control system according to the state of the art by means of which a projectile whose heading is controlled can be made to travel along a squint'or oblique curve.

FIG. 3 is a block diagram of a control system according to thestate of the art be means of which a projectile whose rate of change of heading is controlled can be made to travel along a squint, or oblique, curve, the projectile being controlled directly by the angle 111,, which is measured by the antenna and which is equal to 'itu m h FIG- FIG. 4 is a block diagram of a control system according to the invention by means of which a projectile, whose rate of change of heading is controlled, can be made to travel along a squint, or oblique, curve, the projectile being controlled in response to the behavior of the follow-up system which positions the search head antenna so that the main axis is always directed toward the target.

FIG. 5 is a block diagram of a system which is functionally equivalent to that of FIG. 4.

FIG. 6 shows an apparatus for carrying out the method of the invention by means of which the navigation constant can be switched from K,, l to K,,=l and the constant dc. voltage ll/m1 can be added for a predetermined time interval.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. I shows a typical tactical situation, involving a torpedo T which, while in its autonomously guided phase, is traveling toward a target G. The various horizontal (azimuthal) angles III are shown with respect to true North, the various angles representing the following:

i11 =heading or track made good by the target v,,=speed of the target v ==speed of the torpedo tll =actual heading or track of the torpedo, the same also representing the orientation of the longitudinal axis of the torpedo tll =angle between the longitudinal axis of the torpedo and the main axis of the antenna 111,,=angle of incidence of an incoming signal with respect to the antenna lobe tll =bearing angle of the torpedo to target a =distance between torpedo and target FIG. 2 shows how a course-controlled projectile, such as a torpedo can be guided by adding, after the switch-over from proportional navigation to navigation along a deviated pursuit course has taken place, the constant signal 111,, (a dc. voltage) to the bearing angle 111, which is a mathematical value derived from the kinematic equations (indicated generally by block 2) and which is measured by measuring element 22 and which value is multiplied by the navigation constant K =l in the control circuit 23. This is done in an adder 24 in which there is added to the value K 'lll a constant d.c. electrical quantity representing the squint, or deviation, angle 111 In principle, this addition could be carried out in the comparison element 25 which compares the actual and nominal values ill and 11 respectively. The difference Atlu=rl1,,,=t,l1,,, is applied to the unit 26 which controls the rudder of the torpedo. The actual heading III", of the torpedowhich may be considered to be equal to the course or track made good by the torpedois measured in a known manner by a gyro in the unit 26 and fed back to the comparison element 25. Since 111 is also a mathematical variable in the kinematic equations, it is symbolically fed back, as indicated, to the block 21 representing these equations. The actual heading \,'1,,,(o) at the instant at which the system is switched over from proportional navigation to navigation on a squint, or deviated, angle path is an initial condition of the formal integration from 111 to 41 The addition of the value tl1,,,(o) to the output value is symbolically shown by the adding circle 27 whose output represents the actual course ill, of the torpedo.

In the case of a projectile which is steered not by controlling its heading, but by controlling the rate of change of heading, control after switch-over from proportional navigation to navigation on a deviated pursuit course may be realized by fixing the position of the normally swingably mounted antenna in such a way that the antenna occupies a position with respect to the longitudinal axis of the torpedo which is the nagative of the squint, or deviation, angle #1,. This is possible only if the antenna continues to measure the angle of incidence ll! of the incoming sound waves but is made to influence the movement of the projectile in such a way that n11 becomes equal to zero. The squint angle rule il1,,,=\l1, +111 is then realized by a circuit such as is shown in FIG. 3. The angle of incidence II! can be expressed mathematically as follows:

1,l1 is a predetermined squint angle which is obtained by setting the antenna of the system in such a way that the main axis of the antenna forms this angle with the longitudinal axis of the projectile; this will, in the present case, be equal to the angle +11 described in connection with FIG. 1. In practice, this is done by suitably orienting the antenna of the search head.

Within the imaginary closed heading servo loop, which is obtained as a result of the geometrical condi tions as represented outside of the phantom line in FIG. 3, there is obtained the imaginary nominal heading for the projectile wherein tll is a mathematical quantity obtained from the kinematic equations represented by block 31, and 111 is the squint angle. The addition of both angles is symbolically shown by the summing circle 32. This addition of the squint angle is in fact done not by applying an appropriate electrical signal but is effectively carried out by pivoting the pivotal antenna with respect to the longitudinal axis of the projectile by an appropriate amount. The thus formed, geometrically obtained nominal bearing" 11;, must be reduced by the actual bearing til, to obtain the geometrical quantity 111 This subtraction is again symbolically shown by a summing circle 33. In this way, there is obtained the geometrical angle of incidence 1b,, which is picked up by a phase dis criminator 34 in the sonar head and is there converted into a voltage which is proportional to 111 This value is multiplied in the control circuit 35 by the navigation constant K,, so that there is obtained the nominal value ill, of the rate of change of heading of the projectile. By comparing this nominal value with the actual rate of change of heading ill, in a comparison element 36, there is obtained the deviation A, from the desired nominal value which is equal to di -111 This deviation A111, is applied to the rudder positioning unit 37. The actual rate of change of heading Ji of the projectile is fed back to the comparison element 36 and, after being formally integrated in an integrator 38 and corrected by the actual projectile-to-target bearing lII (O) at the instant of switchover (t=0), is fed back to the kinematic equation block 31 and to the summing circle 33.

Obtaining the value 111,,,=,,,+ at the instant of switch-over from proportional navigation to navigation along a deviated pursuit course, in the manner described above' in connection with FIG. 3, will, in practice, be difficult, because the antenna system of a projectile search head will generally be provided only with a follow-up system for the antenna but there will be no way of fixedly presetting the angle in the projectile, as would have to be done to make the system described in FIG. 3 work. It is for this reason that up to now it was thought in the art that in this case there was no practical way of realizing navigation according to a squint, or deviated, angle curve. On the other hand, for engineering reason, it is better to steer the projectile by controlling the rate of change of heading of the projectile rather than the heading itself. This, then, is where the present invention comes in, in that it provides a practical way in which the impart point of a projectile can be moved ahead, when the following circumstances apply:

a. the projectile is equipped with a passive search head;

b. the projectile is steered by controlling the rate of change of heading;

c. the projectile, during autonomous navigation, is guided under proportional navigation, preferably a navigation constant K,, l; and

d. when the projectile is in the vicinity of the target.

the projectile is to be switched over from proportional navigation to travel along a squint angle curve, the squint angle being such that the first point of intersection of the spiral path strikes the target vessel approximately amidship. ln accordance with the present invention, this is done by making the amplification factor in the control circuit' equal to, i.e., unity gain at the instant of switch-over, and by applying to the guidance system a constant dc. voltage throughout a predetermined, finite time.

FIG. 4 shows one embodiment of an arrangement by means of which the present invention can be carried out. Thus, FIG. 4 is a block diagram for a projectile which is steered by controlling the rate of change of heading and includes a measuring element 42 which measures 4 1 which is the rate of change of heading, this signal being applied to one input of an adder 43, the otherjnput of which has applied to it a constant dc. voltage 111 The output of the adder 43, namely, tll is applied to a control circuit 44 which multiplies this value by the navigation constant K,,=l to produce the nominal rate Ji This value is compared with the actual rate of change III in a comparison element 45, and the difference value Alil =lil lil appearing at the output of the element 45 is applied to the rudder positioning element 46 of the projectile. The value J1, must be formally integrated (indicated by block 47) to obtain, after adding (indicated by adding circle 48) the initial condition tll,,,(o) (which is the actual heading at the instant of change-over), the actual heading 41 which is needed by the kinematic equations (indicated by block 41). The fact that the application of a constant d.c. voltage for a predetermined time interval brings about the desired result is explained in connection with FIG. 5. Assume that, in FIG. 4, all of the elements in the servo loop between the points where the values J1 and 111, appear are linear elementswhich, in pratice, will, for all intents and purposes, be the casethe integration which converts Ill to Ill can be shifted, as shown in FIG. 5, without having any effect whatsoever on the heading 41, FIG. 5 thus shows that the imaginary bearing tl1, =t,l1, (o) was obtained ahead of the adder 43 where lll is added. If the output of the adder is considered to be the nominal heading and if the amplification factor of the control circuit is made equal to ONE, there is obtained which can be recognized as the formula for steering along the squint, or deviated, curve. In order to set the system for a given squint angle d1,,=c l 1,(O), this squint angle must be equal to In the above equations, the angles \11,,,(o), 41,,() and (1%(0) are those angles which hold true at the instant the system is swtiched over from proportional navigation to navigation along a deviated pursuit course.

Inasmuch as tli,,,(o) is already part of the physical structure represented by FIG. 5, namely, in the form of the starting value after the formal integration shown in FIG. 4, the d.c. voltage 11 must be made to equal l'(1isr l'a( in order to obtaina squint angle lll =c't,b,,(o) This means that, in practice, all that has to be done when switching over from proportional navigation to navigation along a deviated pursuit course is to make the amplification factor of the control circuit equal to ONE and to apply a d.c. voltage having an amplitude 111, for a time interval 7 equal to The base of the acoustic of the search head is not adjusted to a constant angle, but continues to operate the follow-up servo loop of the search head as in the case of proportional navigation.

An apparatus for carrying out the method of the invention is shown in FIG. 6.

That apparatus includes an operational amplifier 50 with a normally used feedback resistor 51, which gives an amplification factor of K,, l. Input resistors 52 and 53 are arranged in the input paths of the amplifier 50, to which are applied the signal 41, which is the rate of change of heading, and the constant d.c. voltage di Switches 54 and 55 are simultaneously closed when switch-over from proportional navigation to deviate persuit course takes place. In that instant of switchover a resistor 56, arranged in a path parallel to the amplifier 50 and the feedback resistor 51, respectively, is added, so that the combination of both resistors 51 and 56 has a value less than the value of the feedback resistor 51 alone. Thus, by choosing the value of the resistor 56, it can be obtained that the parallel combination of the resistors 51 and 56 gives an amplification factor K,,=l.

The d.c. voltage Mi has been applied to the amplifier 50 due to the closure of the switch 54. Then the output of the amplifier 50 is equal to By comparing the apparatus of FIG. 6 with the symbolic block diagram of FIG. 4 it will be seen, that amplifier 50 with its input and feedback resistors represents the adder 43 and the guidance control circuit 44. The following amplifier 57 represents the comparison element 45 of FIG. 4.

It will be understood that the above description of the present invention is susceptible to various modifications, changes and adaptations and the same are intended to be comprehended within the meaning and range of equivalents of the appended claims.

I claim:

I. In a method for advancing the impact point of a projectile equipped with a passive search head, which projectile is steered by controlling the rate of change of the projectile-to-target heading and, during the autonomous phase, by proportional navigation, wherein, in the vicinity of the barget, there is a switch-over from proportional navigation to navigation along a deviated pursuit course wherein the squint angle is such that the first point of intersection of the spiral path with the track being made good by the target is approximately amidship of the target, the improvement comprising the steps of setting the amplification of the control circuit to unity gain at the instant of switch-over from proportional navigation to navigation along a deviated pursuit course, and applying to the control circuit a constant d.c. voltage throughout a predetermined, finite time interval, with the magnitude of said d.c. voltage and said time interval being selected to produce the desired squint angle.

2. The method as defined in claim 1 wherein: the rate of change of the projectile-to-target heading is measured and a signal proportional thereto produced and integrated; the integrated rate of change of projectileto-target heading signal is fed to the input of the control circuit; and said step of applying includes integrating said constant d.c. voltage throughout said time interval and adding the integrated constant d.c. voltage signal to the integrated rate of change of projectile-to-target heading signal at the input of the control circuit, said integrated d.c. voltage signal having a value equal to where (11,,(0) is the angle between the main axis of the search head and the main axis of the projectile at the instant of switching from proportional navigation to navigation along a deviated pursuit course and c is a constant which is selected to satisfy the equation t11 =c 1b,,(o) where di is the desired squint angle.

3. The method as defined in claim 1 wherein said d.c. voltage (111. and said time interval r are such that the product of both satisfies the equation:

where min, (0) is the angle between the main axis of the search head and the main axis of the projectile at the instant of switching from proportional navigation to navigation along a deviated pursuit course and 4: is the desired squint angle.

4. In a method for moving ahead the impact point of a projectile equipped with a passive search head, which projectile is steered by controlling the rate of change of the projectile-totarget heading and, during the autonomous phase, by proportional navigation, wherein the distance between the projectile and the target is determined and, at a suitable point in the vicinity of the target, there is a switch-over from proportional navigation to navigation along a deviated pursuit course, and wherein the squint angle is such that the first point of intersection of the spiral path with the track being made good by the target is approximately amidship of the target, the improvement comprising the following steps after switch-over to navigation along a deviated pursuit course:

a. producing a signal representing the rate of change navigation constant equal to ONE to produce a sigof the projectile-to-target heading; nal representing the nominal rate of change of b. adding a dc. voltage signal related to a desired heading; squint angle to the rate ofchange of heading signal, d. measuring the actual rate of change of heading of said dc. voltage signal (ti/ being related to the the projectile and producing a signal representative desired squint angle according to the following rethereof; lationship e. comparing the signal produced in step (c) with said signal representing the actual rate of change of heading of the projectile and producing a differwhere 41 (o) is the angle between the main axis of the ence signal; and search head and the main axis of the projectile at the f. steering the projectile in response to said difference instant of switching from proportional navigation to signal. navigation along a deviated pursuit course, 41,, is the de- 5. The method defined in claim 4 wherein the projecsired squint angle, and r is the time interval during tile is a torpedo and where said step (e) is carried out which the dc. voltage is applied; 5 by positioning the rudder of the torpedo.

c. multiplying the signal produced in step (b) by a 

1. In a method for advancing the impact point of a projectile equipped with a passive search head, which projectile is steered by controlling the rate of change of the projectile-to-target heading and, during the autonomous phase, by proportional navigation, wherein, in the vicinity of the barget, there is a switch-over from proportional navigation to navigation along a deviated pursuit course wherein the squint angle is such that the first point of intersection of the spiral path with the track being made good by the target is approximately amidship of the target, the improvement comprising the steps of setting the amplification of the control circuit to unity gain at the instant of switch-over from proportional navigation to navigation along a deviated pursuit course, and applying to the control circuit a constant d.c. voltage throughout a predetermined, finite time interval, with the magnitude of said d.c. voltage and said time interval being selected to produce the desired squint angle.
 2. The method as defined in claim 1 wherein: the rate of change of the projectile-to-target heading is measured and a signal proportional thereto produced and integrated; the integrated rate of change of projectile-to-target heading signal is fed to the input of the control circuit; and saiD step of applying includes integrating said constant d.c. voltage throughout said time interval and adding the integrated constant d.c. voltage signal to the integrated rate of change of projectile-to-target heading signal at the input of the control circuit, said integrated d.c. voltage signal having a value equal to (1+c). psi b(o) where psi b(o) is the angle between the main axis of the search head and the main axis of the projectile at the instant of switching from proportional navigation to navigation along a deviated pursuit course and c is a constant which is selected to satisfy the equation psi o c psi b(o) where psi o is the desired squint angle.
 3. The method as defined in claim 1 wherein said d.c. voltage ( psi dist) and said time interval Tau are such that the product of both satisfies the equation: Tau . psi dist psi b (o)+ psi o where psi b (o) is the angle between the main axis of the search head and the main axis of the projectile at the instant of switching from proportional navigation to navigation along a deviated pursuit course and psi o is the desired squint angle.
 4. In a method for moving ahead the impact point of a projectile equipped with a passive search head, which projectile is steered by controlling the rate of change of the projectile-to-target heading and, during the autonomous phase, by proportional navigation, wherein the distance between the projectile and the target is determined and, at a suitable point in the vicinity of the target, there is a switch-over from proportional navigation to navigation along a deviated pursuit course, and wherein the squint angle is such that the first point of intersection of the spiral path with the track being made good by the target is approximately amidship of the target, the improvement comprising the following steps after switch-over to navigation along a deviated pursuit course: a. producing a signal representing the rate of change of the projectile-to-target heading; b. adding a d.c. voltage signal related to a desired squint angle to the rate of change of heading signal, said d.c. voltage signal ( psi dist) being related to the desired squint angle according to the following relationship Tau . psi dist psi b(o)+ psi o where where psi b (o) is the angle between the main axis of the search head and the main axis of the projectile at the instant of switching from proportional navigation to navigation along a deviated pursuit course, psi o is the desired squint angle, and Tau is the time interval during which the d.c. voltage is applied; c. multiplying the signal produced in step (b) by a navigation constant equal to ONE to produce a signal representing the nominal rate of change of heading; d. measuring the actual rate of change of heading of the projectile and producing a signal representative thereof; e. comparing the signal produced in step (c) with said signal representing the actual rate of change of heading of the projectile and producing a difference signal; and f. steering the projectile in response to said difference signal.
 5. The method defined in claim 4 wherein the projectile is a torpedo and where said step (e) is carried out by positioning the rudder of the torpedo. 